GA pilot reported a NMAC in the traffic pattern when an aircraft flew under them; then circled back for landing without making any position announcements.

Narrative

Announced position 10 miles south ZZZ planning midfield cross to left downwind for [Runway] XX. Announced crossing midfield to left downwind for XX. Wind 130@ 3 kts. Just crossed midfield south to north and left hand turn to downwind; see aircraft approx 1 mile @ 12 oclock. Heard no announcement by other aircraft. No aircraft on my ADSB display or my TCAS. I confirmed I was on correct frequency for CTAF. I held altitude and speed of 110 kias. Once i visually confirmed it was indeed an aircraft flying towards me/ towards runway from right to left; i was about to evade to a climbing right turn; when i could see it was crossing about 300 ft in front of me and approximately 300 feet below me (from NW to SE crossing the downwind and runway to opposite side). I was headed west ( heading of 270). I could see his numbers. I was able to finish my downwind; base; and final and have an uneventful landing. While rolling out i heard the first radio call by the plane now coming back north to cross midfield to left downwind for 10. I taxied to my hangar; put my plane away. After Aircraft Y landed and taxied to his hangar and was out of his plane; i calmly went to see him. I told him he needed to check his transponder since i had no traffic display for him and also he must have an intermittent radio issue as well. He stated he heard me call my position in the traffic pattern. He had no idea he flew in front and below me while crossing the field at below pattern altitude. I left it at that I realize there was nothing illegal here - he doesn't have to announce at untowered field. Seems like a real dangerous way to fly - crossing midfield below pattern altitude in the wrong direction WHILE SOMEONE IS IN THE DOWNWIND; WITHIN 500 ft of your position; only to do a 180 turn and cross back across midfield. I didn't get the impression he felt he did anything wrong or unsafe. Seems like an accident waiting to happen with this individual.